Banach空间阻尼弹性系统L-拟mild解的存在性

摘要/Abstract

摘要：

该文讨论了Banach空间中具有阻尼弹性系统L-拟mild解的存在性.这些结果改进和推广了一些相关的结论在常微分方程和偏微分方程方面.在非线性项满足单调条件和非紧性测度条件下，获得了该问题极大mild解的存在性.另外，给出例子说明该结果的可行性.

关键词: 弹性系统, mild解, L-拟上下解, 非紧性测度

Abstract:

In this article, we deals with the existence of L-quasi mild solutions for damped elastic systems in Banach spaces. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. Under monotone condition and the noncompactness measure condition on nonlinearity, we obtain the existence of extremal mild solutions. In addition, an example is given to illustrate our results.

Key words: Damped elastic systems, Mild solution, Lower and upper L-quasi solutions, Measure of noncompactness

中图分类号:

O175.15

苟海德. Banach空间阻尼弹性系统L-拟mild解的存在性[J]. 数学物理学报, 2020, 40(2): 408-421.

Haide Gou. Existence of L-Quasi Mild Solutions for Damped Elastic Systems in Banach Spaces[J]. Acta mathematica scientia,Series A, 2020, 40(2): 408-421.

参考文献 20

1	Chen G , Russell D L . A mathematical model for linear elastic systems with structural damping. Quarterly of Applied Mathematics, 1982, 39, 433- 454 doi: 10.1090/qam/644099
2	Huang F . On the holomorphic property of the semigroup associated with linear elastic systems with structural damping. Acta Mathematica Scientia, 1985, 5, 271- 277 doi: 10.1016/S0252-9602(18)30548-4
3	Huang F . A problem for linear elastic systems with structural damping. Acta Math Ematica Scientia, 1986, 6, 101- 107
4	Chen S , Triggiani R . Proof of extensions of two conjectures on structural damping for elastic systems:the systems:the case 1/2 < α ≤ 1. Pacific Journal of Mathematics, 1989, 136, 15- 55 doi: 10.2140/pjm.1989.136.15
5	Chen S , Triggiani R . Gevrey class semigroups arising from elastic systems with gentle dissipation:the case 0 < α < 1. Proceedings of the American Mathmematical Society, 1990, 110, 401- 415
6	Huang F L . On the mathematical model for linear elastic systems with analytic damping. SIAM Journal on Control and Optimization, 1988, 26, 714- 724 doi: 10.1137/0326041
7	Liu K , Liu Z . Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces. Journal of Differential Equations, 1997, 141, 340- 355 doi: 10.1006/jdeq.1997.3331
8	Huang F , Liu K . Holomorphic property and exponential stability of the semigroup associated with linear elastic systems with damping. Annals of Differential Equations, 1988, 4, 411- 424
9	Huang F , Huang Y , Guo F . Holomorphic and differentiable properties of the C₀-semigroup associated with the Euler-Bernoulli beam equations with structural damping. Science in China, 1992, 35, 547- 560
10	Huang F , Liu K , Chen G . Differentiability of the semigroup associated with a structural damping model//Tampa, FL:IEEE. Proceedings of the 28th IEEE Conference on Decision and Control (IEEE-CDC 1989), 1989, 2034- 2038
11	Fan H , Li Y . Analyticity and exponential stability of semigroup for elastic systems with structural damping in Banach spaces. J Math Anal Appl, 2014, 410, 316- 322 doi: 10.1016/j.jmaa.2013.08.028
12	Fan H , Gao F . Asymptotic stability of solutions to elastic systems with structural damping. Electron J Differential Equations, 2014, 245, 9
13	Fan H, Li Y, Chen P. Existence of mild solutions for the elastic systems with structural damping in Banach spaces. Abstract and Applied Analysis, 2013, Article ID: 746893
14	Banas J, Goebel K. Measures of Noncompactness in Banach Spaces. New York: Marcel Dekker, 1980
15	Deimling K. Nonlinear Functional Analysis. New York: Springer-Verlag, 1985
16	Heinz H P . On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions. Nonlinear Anal, 1983, 7, 1351- 1371 doi: 10.1016/0362-546X(83)90006-8
17	李永祥. 抽象半线性发展方程初值问题解的存在性. 数学学报, 2005, 48, 1089- 1094 doi: 10.3321/j.issn:0583-1431.2005.06.006
	Li Y . Existence of solutions of initial value problems for abstract semilinear evolution equations. Acta Math Sin, 2005, 48, 1089- 1094 doi: 10.3321/j.issn:0583-1431.2005.06.006
18	Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Berlin: Springer, 1983
19	李永祥. 抽象半线性发展方程的正解及其应用. 数学学报, 1996, 39, 666- 672
	Li Y . The positive solutions of abstract semilinear evolution equations and their applications. Acta Math Sin, 1996, 39, 666- 672
20	Du Y . Fixed points of increasing operators in Banach spaces and applications. Appl Anal, 1990, 38, 1- 20 doi: 10.1080/00036819008839957

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